$ \left(\dfrac{64}{125}\right)^{-\frac{1}{3}}$
$= \left(\dfrac{125}{64}\right)^{\frac{1}{3}}$ Figure out what goes in the blank: $\Big(? \Big)^{3}=\dfrac{125}{64}$ Figure out what goes in the blank: $\Big({\dfrac{5}{4}}\Big)^{3}=\dfrac{125}{64}$ So $\left(\dfrac{64}{125}\right)^{-\frac{1}{3}}=\left(\dfrac{125}{64}\right)^{\frac{1}{3}}=\dfrac{5}{4}$